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Popular >

(d^2y)/(dx^2)+2(dy)/(dx)-15y=7+4x

Solution

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 15 y = 7 + 4 x

Solution

y = c_{1} e^{3 x} + c_{2} e^{- 5 x} - \frac{4 x}{15} - \frac{113}{225}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 15 y = 7 + 4 x

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 5 x} - \frac{4 x}{15} - \frac{113}{225}

y = c_{1} e^{3 x} + c_{2} e^{- 5 x} - \frac{4 x}{15} - \frac{113}{225}

Popular Examples

y^{''}+4y=-5sin(2t)+2cos(2t)

y^{^{''}} + 4 y = - 5 sin (2 t) + 2 cos (2 t)

(d^2y)/(dx^2)-2(dy)/(dx)=2e^{2x}

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} = 2 e^{2 x}

(d^2y)/(dt^2)+8(dy)/(dt)+15y=3

\frac{d ^{2} y}{d t ^{2}} + 8 \frac{d y}{d t} + 15 y = 3

y^{''}-6y^'-27y=-57t+54t^2

y^{^{''}} - 6 y^{^{'}} - 27 y = - 57 t + 54 t^{2}

y^{''}+15y^'+56y=112x^2+60x+4+72e^x

y^{^{''}} + 15 y^{^{'}} + 56 y = 112 x^{2} + 60 x + 4 + 72 e^{x}

Frequently Asked Questions (FAQ)

What is the solution for (d^2y)/(dx^2)+2(dy)/(dx)-15y=7+4x ?
The solution for (d^2y)/(dx^2)+2(dy)/(dx)-15y=7+4x is y=c_{1}e^{3x}+c_{2}e^{-5x}-(4x)/(15)-113/225