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Differential EquationQuestion and Answers: Page 1

Question Number 218396 Answers: 0 Comments: 0

Question Number 217797 Answers: 3 Comments: 0

Solve: 5x^2 y′′ + x(1 + x) y′ − y = 0

$$\mathrm{Solve}: \\ $$$$\:\:\:\:\:\mathrm{5x}^{\mathrm{2}} \:\mathrm{y}''\:\:+\:\:\:\mathrm{x}\left(\mathrm{1}\:\:+\:\:\mathrm{x}\right)\:\mathrm{y}'\:\:−\:\:\mathrm{y}\:\:\:=\:\:\:\mathrm{0} \\ $$

Question Number 217245 Answers: 1 Comments: 0

find the following differential equation by eliminating the arbritrary constant (1)y=Ae^x +Bcosx (2) xy=Ae^x +Be^(−x) +x^2

$${find}\:{the}\:{following}\:{differential}\:{equation}\: \\ $$$${by}\:{eliminating}\:{the}\:{arbritrary}\:{constant} \\ $$$$\left(\mathrm{1}\right){y}={Ae}^{{x}} +{Bcosx} \\ $$$$\left(\mathrm{2}\right)\:{xy}={Ae}^{{x}} +{Be}^{−{x}} +{x}^{\mathrm{2}} \\ $$$$ \\ $$

Question Number 217046 Answers: 1 Comments: 0

form the differential equation by eliminating the arbritrary constant y^2 =Ax^2 +Bx+C

$${form}\:{the}\:{differential}\:{equation}\:{by}\: \\ $$$${eliminating}\:{the}\:{arbritrary}\:{constant} \\ $$$${y}^{\mathrm{2}} ={Ax}^{\mathrm{2}} +{Bx}+{C} \\ $$

Question Number 216787 Answers: 1 Comments: 0

form the differential equationfrom the following 1) y=Ae^(3x) +Be^(5x) 2) y^2 =(x−1) 3) c(y+c)^2 +x^3 =0

$${form}\:{the}\:{differential}\:{equationfrom}\:{the}\:{following} \\ $$$$\left.\mathrm{1}\right)\:{y}={Ae}^{\mathrm{3}{x}} +{Be}^{\mathrm{5}{x}} \\ $$$$\left.\mathrm{2}\right)\:{y}^{\mathrm{2}} =\left({x}−\mathrm{1}\right) \\ $$$$\left.\mathrm{3}\right)\:{c}\left({y}+{c}\right)^{\mathrm{2}} +{x}^{\mathrm{3}} =\mathrm{0} \\ $$

Question Number 215468 Answers: 2 Comments: 0

((∂xω)/(∂yω))∙(∂e/∂ω)=? x=f(y) ω=g(y) e=h(ω)

$$\frac{\partial{x}\omega}{\partial{y}\omega}\centerdot\frac{\partial{e}}{\partial\omega}=? \\ $$$${x}={f}\left({y}\right) \\ $$$$\omega={g}\left({y}\right) \\ $$$${e}={h}\left(\omega\right) \\ $$

Question Number 214813 Answers: 1 Comments: 1

Help me solve this (dy/dx)+(a/y)+b(√x)=0

$${Help}\:{me}\:{solve}\:{this} \\ $$$$\frac{{dy}}{{dx}}+\frac{{a}}{{y}}+{b}\sqrt{{x}}=\mathrm{0} \\ $$

Question Number 213097 Answers: 1 Comments: 0

Uhhhh. can you guys solve Partial differantial equation ▽^2 𝛗=0 Cylinderical Laplacian case ▽^2 =(1/ρ)∙((∂ )/∂ρ)(ρ((∂ )/∂ρ))+((1/ρ))^2 (∂^2 /∂φ^2 )+((∂^2 )/∂z^2 ) Spherical Laplacian case ▽^2 =((1/r))^2 ((∂ )/∂r)(r^2 ((∂ )/∂r))+(1/(r^2 sin(θ)))∙((∂ )/∂θ)(sin(θ)((∂ )/∂θ))+(1/(r^2 sin^2 (θ)))∙(∂^2 /∂ϕ^2 )

$$\mathrm{Uhhhh}. \\ $$$$\mathrm{can}\:\mathrm{you}\:\mathrm{guys}\:\mathrm{solve}\:\mathrm{Partial}\:\mathrm{differantial}\:\mathrm{equation} \\ $$$$\bigtriangledown^{\mathrm{2}} \boldsymbol{\phi}=\mathrm{0} \\ $$$$\mathrm{Cylinderical}\:\mathrm{Laplacian}\:\mathrm{case} \\ $$$$\bigtriangledown^{\mathrm{2}} =\frac{\mathrm{1}}{\rho}\centerdot\frac{\partial\:\:}{\partial\rho}\left(\rho\frac{\partial\:\:}{\partial\rho}\right)+\left(\frac{\mathrm{1}}{\rho}\right)^{\mathrm{2}} \frac{\partial^{\mathrm{2}} \:}{\partial\phi^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} \:\:}{\partial{z}^{\mathrm{2}} } \\ $$$$\mathrm{Spherical}\:\mathrm{Laplacian}\:\mathrm{case} \\ $$$$\bigtriangledown^{\mathrm{2}} =\left(\frac{\mathrm{1}}{{r}}\right)^{\mathrm{2}} \frac{\partial\:\:}{\partial{r}}\left({r}^{\mathrm{2}} \frac{\partial\:\:}{\partial{r}}\right)+\frac{\mathrm{1}}{{r}^{\mathrm{2}} \mathrm{sin}\left(\theta\right)}\centerdot\frac{\partial\:\:}{\partial\theta}\left(\mathrm{sin}\left(\theta\right)\frac{\partial\:\:}{\partial\theta}\right)+\frac{\mathrm{1}}{{r}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \left(\theta\right)}\centerdot\frac{\partial^{\mathrm{2}} \:}{\partial\varphi^{\mathrm{2}} } \\ $$

Question Number 212895 Answers: 0 Comments: 0

Question Number 213371 Answers: 0 Comments: 1

Question Number 212435 Answers: 1 Comments: 0

Question Number 212307 Answers: 1 Comments: 0

I=∫_0 ^∞ (((x−arctan x)^2 )/x^4 )dx.

$$ \\ $$$$\:\:{I}=\int_{\mathrm{0}} ^{\infty} \frac{\left({x}−\mathrm{arctan}\:{x}\right)^{\mathrm{2}} }{{x}^{\mathrm{4}} }{dx}. \\ $$

Question Number 212141 Answers: 2 Comments: 0

∫((cos^2 x)/(sin x+cos x))dx.

$$ \\ $$$$\:\:\:\:\:\:\:\:\int\frac{\mathrm{cos}^{\mathrm{2}} {x}}{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{dx}. \\ $$$$ \\ $$

Question Number 212107 Answers: 1 Comments: 0

I=∫_0 ^∞ ((x cos x−sin x)/x^2 )dx.

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{I}=\int_{\mathrm{0}} ^{\infty} \frac{{x}\:\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}{{x}^{\mathrm{2}} }{dx}. \\ $$$$ \\ $$

Question Number 211738 Answers: 0 Comments: 1

∫(1/(x^5 +1 ))dx.

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{\mathrm{1}}{\boldsymbol{{x}}^{\mathrm{5}} +\mathrm{1}\:}\boldsymbol{{dx}}. \\ $$$$ \\ $$

Question Number 211703 Answers: 0 Comments: 2

Calculate the quadruple integralas follows: I=∫_0 ^1 ∫_0 ^x ∫_0 ^y ∫_0 ^z ((sin(x^2 +y^2 +z^2 +w^2 ))/(1+w^2 +z^2 ))dw dz dy dx

$$ \\ $$$$\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{quadruple}\: \\ $$$$\mathrm{integralas}\:\mathrm{follows}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\boldsymbol{{x}}} \int_{\mathrm{0}} ^{\boldsymbol{\mathrm{y}}} \int_{\mathrm{0}} ^{\boldsymbol{{z}}} \frac{\boldsymbol{\mathrm{sin}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}} +\boldsymbol{{w}}^{\mathrm{2}} \right)}{\mathrm{1}+\boldsymbol{{w}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}} }\boldsymbol{{dw}}\:\boldsymbol{{dz}}\:\boldsymbol{\mathrm{dy}}\:\boldsymbol{{dx}} \\ $$$$ \\ $$

Question Number 211579 Answers: 2 Comments: 0

∫(1/((1−x^4 )(√(1+x^2 ))))dx.

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{\mathrm{1}}{\left(\mathrm{1}−\boldsymbol{{x}}^{\mathrm{4}} \right)\sqrt{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} }}\boldsymbol{{dx}}. \\ $$$$ \\ $$

Question Number 211560 Answers: 0 Comments: 0

certificate: I=∫_0 ^(𝛑/2) (√(√(x^2 +ln^2 cos(x)−lncos(x)dx)))=(𝛑/2)(√(2ln2))

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{certificate}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \sqrt{\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{ln}}^{\mathrm{2}} \boldsymbol{\mathrm{cos}}\left(\boldsymbol{{x}}\right)−\boldsymbol{\mathrm{lncos}}\left(\boldsymbol{{x}}\right)\boldsymbol{{dx}}}}=\frac{\boldsymbol{\pi}}{\mathrm{2}}\sqrt{\mathrm{2}\boldsymbol{\mathrm{ln}}\mathrm{2}} \\ $$$$ \\ $$

Question Number 211546 Answers: 2 Comments: 0

∫(dx/( (√(x^2 −4x+13))))=?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{\boldsymbol{{dx}}}{\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{{x}}+\mathrm{13}}}=? \\ $$

Question Number 210786 Answers: 1 Comments: 0

Question Number 208739 Answers: 0 Comments: 0

Question Number 208569 Answers: 0 Comments: 0

help me to solve this please y′′−(√(1+y′^2 ))=x^2 solve this differential equation

$$\boldsymbol{{help}}\:\boldsymbol{{me}}\:\boldsymbol{{to}}\:\boldsymbol{{solve}}\:\boldsymbol{{this}}\:\boldsymbol{{please}} \\ $$$$\:\:\boldsymbol{{y}}''−\sqrt{\mathrm{1}+\boldsymbol{{y}}'^{\mathrm{2}} }=\boldsymbol{{x}}^{\mathrm{2}} \\ $$$$\boldsymbol{{solve}}\:\boldsymbol{{this}}\:\boldsymbol{{differential}}\:\boldsymbol{{equation}} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 208303 Answers: 1 Comments: 0

Resolver (∂^2 u/∂y^2 ) − x^2 u = xe^(4y)

$${Resolver} \\ $$$$\frac{\partial^{\mathrm{2}} {u}}{\partial{y}^{\mathrm{2}} }\:−\:{x}^{\mathrm{2}} {u}\:=\:{xe}^{\mathrm{4}{y}} \\ $$

Question Number 208264 Answers: 1 Comments: 0

$$\:\:\:\cancel{\underline{\underbrace{ }}} \\ $$

Question Number 207991 Answers: 2 Comments: 0

y W

$$\:\:\:\:\:\mathrm{y}\:\underline{\underbrace{\mathcal{W}}} \\ $$

Question Number 207317 Answers: 2 Comments: 0

solve for y (1/(y′))+(1/(y′′))=1

$${solve}\:{for}\:{y} \\ $$$$\frac{\mathrm{1}}{{y}'}+\frac{\mathrm{1}}{{y}''}=\mathrm{1} \\ $$

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