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Popular >

x^{''}+x^'=t

Solution

x^{^{''}} + x^{^{'}} = t

Solution

x = c_{1} + c_{2} e^{- t} + \frac{t ^{2}}{2} - t

Solution steps

x^{''} (t) + x^{'} (t) = t

Solve linear ODE:

x = c_{1} + c_{2} e^{- t} + \frac{t ^{2}}{2} - t

x = c_{1} + c_{2} e^{- t} + \frac{t ^{2}}{2} - t

Graph

Popular Examples

(d^2-1)y=x^2e^x

(d^{2} - 1) y = x^{2} e^{x}

y^{'''}+10y^{''}+33y^'+36y=4te^t

y^{^{'''}} + 10 y^{^{''}} + 33 y^{^{'}} + 36 y = 4 t e^{t}

x^{''}+4x^'-5x=4t^2

x^{^{''}} + 4 x^{^{'}} - 5 x = 4 t^{2}

2y^{''}+2y^'+5y=cos(x)-5sin(x)

2 y^{^{''}} + 2 y^{^{'}} + 5 y = cos (x) - 5 sin (x)

y^{''}-2y^'+y=2sin(t),y^'(0)=1,y(0)=2

y^{^{''}} - 2 y^{^{'}} + y = 2 sin (t), y^{^{'}} (0) = 1, y (0) = 2

Frequently Asked Questions (FAQ)

What is the solution for x^{''}+x^'=t ?
The solution for x^{''}+x^'=t is x=c_{1}+c_{2}e^{-t}+(t^2)/2-t