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Popular >

y^{''''}-2y^{'''}+y^{''}=e^x+1

Solution

y^{^{''''}} - 2 y^{^{'''}} + y^{^{''}} = e^{x} + 1

Solution

y = c_{1} + c_{2} x + c_{3} e^{x} + c_{4} x e^{x} + \frac{e ^{x} x ^{2} + x ^{2}}{2}

Solution steps

y^{(4)} (x) - 2 y^{'''} (x) + y^{''} (x) = e^{x} + 1

Solve linear ODE:

y = c_{1} + c_{2} x + c_{3} e^{x} + c_{4} x e^{x} + \frac{e ^{x} x ^{2} + x ^{2}}{2}

y = c_{1} + c_{2} x + c_{3} e^{x} + c_{4} x e^{x} + \frac{e ^{x} x ^{2} + x ^{2}}{2}

Popular Examples

y^{''}+6y^'-7y=3e^{2x}-e^{-x}

y^{^{''}} + 6 y^{^{'}} - 7 y = 3 e^{2 x} - e^{- x}

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

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

y^{''}-2y^'-3y=12e^x-6

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e^{x} - 6

y^{''}+y=xcos(x)-cos(x)

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

y^{''}-10y^'+9y=5t

y^{^{''}} - 10 y^{^{'}} + 9 y = 5 t

Frequently Asked Questions (FAQ)

What is the solution for y^{''''}-2y^{'''}+y^{''}=e^x+1 ?
The solution for y^{''''}-2y^{'''}+y^{''}=e^x+1 is y=c_{1}+c_{2}x+c_{3}e^x+c_{4}xe^x+(e^xx^2+x^2)/2