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Popular Calculus >

y^{''}+3y^'-7y=t^4e^t

Solution

y^{^{''}} + 3 y^{^{'}} - 7 y = t^{4} e^{t}

Solution

y = c_{1} e^{\frac{( - 3 + 37 ) t}{2}} + c_{2} e^{\frac{( - 3 - 37 ) t}{2}} - \frac{e ^{t} t ^{4}}{3} - \frac{20 e ^{t} t ^{3}}{9} - \frac{112 e ^{t} t ^{2}}{9} - \frac{1240 e ^{t} t}{27} - \frac{6872}{81} e^{t}

Solution steps

y^{''} (t) + 3 y^{'} (t) - 7 y = t^{4} e^{t}

Solve linear ODE:

y = c_{1} e^{\frac{( - 3 + 37 ) t}{2}} + c_{2} e^{\frac{( - 3 - 37 ) t}{2}} - \frac{e ^{t} t ^{4}}{3} - \frac{20 e ^{t} t ^{3}}{9} - \frac{112 e ^{t} t ^{2}}{9} - \frac{1240 e ^{t} t}{27} - \frac{6872}{81} e^{t}

y = c_{1} e^{\frac{( - 3 + 37 ) t}{2}} + c_{2} e^{\frac{( - 3 - 37 ) t}{2}} - \frac{e ^{t} t ^{4}}{3} - \frac{20 e ^{t} t ^{3}}{9} - \frac{112 e ^{t} t ^{2}}{9} - \frac{1240 e ^{t} t}{27} - \frac{6872}{81} e^{t}

Graph

Popular Examples

x^{''}-16x^'+64x=te^{8t}

0.5y^{''}+5y^'+12y=e^{-4t}(4t-2)

y^{''}+2y^'-3y=e^{2t}-2t

x^{''}+36x=8cos(6t)

y^{''}-3y^'+2y=7x+28

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+3y^'-7y=t^4e^t ?
The solution for y^{''}+3y^'-7y=t^4e^t is