What is the solution for y^{''}-7y^'=49t,y(0)=7,y^'(0)=0 ?

The solution for y^{''}-7y^'=49t,y(0)=7,y^'(0)=0 is y=(7-48/7)e^{7t}+48/7-(7t^2)/2-t

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y^{''}-7y^'=49t,y(0)=7,y^'(0)=0

y^{^{''}} - 7 y^{^{'}} = 49 t, y (0) = 7, y^{^{'}} (0) = 0

y = (7 - \frac{48}{7}) e^{7 t} + \frac{48}{7} - \frac{7 t ^{2}}{2} - t

Solution steps

y^{''} (t) - 7 y^{'} (t) = 49 t

Solve linear ODE:

y = (7 - \frac{48}{7}) e^{7 t} + \frac{48}{7} - \frac{7 t ^{2}}{2} - t

y = (7 - \frac{48}{7}) e^{7 t} + \frac{48}{7} - \frac{7 t ^{2}}{2} - t

x \to 0 lim (\frac{1}{x ^{2}})

y^{^{''}} + 4 y^{^{'}} + 5 y = 35 e^{- 4 x}, y (0) = - 2, y^{^{'}} (0) = 1

x \to 0 lim ((1 + x^{2}) - 1)

\frac{d}{d x} (cos^{2} (x) sin (x))

(x^{3} + 5) e x

What is the solution for y^{''}-7y^'=49t,y(0)=7,y^'(0)=0 ?
The solution for y^{''}-7y^'=49t,y(0)=7,y^'(0)=0 is y=(7-48/7)e^{7t}+48/7-(7t^2)/2-t