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Popular >

y^{'''}-y^{''}=3e^x+sin(x)

Solution

y^{^{'''}} - y^{^{''}} = 3 e^{x} + sin (x)

Solution

y = c_{1} e^{x} + c_{2} + c_{3} x + 3 x e^{x} + \frac{1}{2} sin (x) + \frac{1}{2} cos (x)

Solution steps

y^{'''} (x) - y^{''} (x) = 3 e^{x} + sin (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} + c_{3} x + 3 x e^{x} + \frac{1}{2} sin (x) + \frac{1}{2} cos (x)

y = c_{1} e^{x} + c_{2} + c_{3} x + 3 x e^{x} + \frac{1}{2} sin (x) + \frac{1}{2} cos (x)

Graph

Popular Examples

y^{''}-14*y^{''}+45*y^'=32e^x

y^{^{''}} - 14 \cdot y^{^{''}} + 45 \cdot y^{^{'}} = 32 e^{x}

y^{''}-y^'-6y=4te^3t,y(0)=-5,y^'(0)=-3

y^{^{''}} - y^{^{'}} - 6 y = 4 t e^{3} t, y (0) = - 5, y^{^{'}} (0) = - 3

y^{''}+y^'-2y=-4,y(0)=2,y^'(0)=3

y^{^{''}} + y^{^{'}} - 2 y = - 4, y (0) = 2, y^{^{'}} (0) = 3

-y^{''}+y^'+2y=e^t

- y^{^{''}} + y^{^{'}} + 2 y = e^{t}

y^{''}-4y^'-21y=800e^{-t}

y^{^{''}} - 4 y^{^{'}} - 21 y = 800 e^{- t}

Frequently Asked Questions (FAQ)

What is the solution for y^{'''}-y^{''}=3e^x+sin(x) ?
The solution for y^{'''}-y^{''}=3e^x+sin(x) is y=c_{1}e^x+c_{2}+c_{3}x+3xe^x+1/2 sin(x)+1/2 cos(x)