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Popular >

y^{''}+6y^'+3x=0,y(0)=0,y^'(0)=1

Solution

y^{^{''}} + 6 y^{^{'}} + 3 x = 0, y (0) = 0, y^{^{'}} (0) = 1

Solution

y = \frac{11}{72} - \frac{11}{72} e^{- 6 x} - \frac{x ^{2}}{4} + \frac{x}{12}

Solution steps

y^{''} (x) + 6 y^{'} (x) + 3 x = 0

Solve linear ODE:

y = \frac{11}{72} - \frac{11}{72} e^{- 6 x} - \frac{x ^{2}}{4} + \frac{x}{12}

y = \frac{11}{72} - \frac{11}{72} e^{- 6 x} - \frac{x ^{2}}{4} + \frac{x}{12}

Graph

Popular Examples

y^{''}+5y=5sin(x),y(0)=1,y^'(0)=2

y^{^{''}} + 5 y = 5 sin (x), y (0) = 1, y^{^{'}} (0) = 2

y^{'''}+y^'=sec(t),y^'(0)=3,y^{''}(0)=-2

y^{^{'''}} + y^{^{'}} = sec (t), y^{^{'}} (0) = 3, y^{^{''}} (0) = - 2

(d^2y)/(dx^2)-2*(dy)/(dx)+y=(x-1)*e^x

\frac{d ^{2} y}{d x ^{2}} - 2 \cdot \frac{d y}{d x} + y = (x - 1) \cdot e^{x}

(d^2y)/(dx^2)+(dy)/(dx)=sin(x)

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} = sin (x)

y^{''}-81y=e^{9x}

y^{^{''}} - 81 y = e^{9 x}

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+6y^'+3x=0,y(0)=0,y^'(0)=1 ?
The solution for y^{''}+6y^'+3x=0,y(0)=0,y^'(0)=1 is y= 11/72-11/72 e^{-6x}-(x^2)/4+x/(12)