What is the solution for (d^3y)/(dx^3)-(d^2y)/(dx^2)=0 ?

The solution for (d^3y)/(dx^3)-(d^2y)/(dx^2)=0 is y=c_{1}e^x+c_{2}+c_{3}x

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(d^3y)/(dx^3)-(d^2y)/(dx^2)=0

\frac{d ^{3} y}{d x ^{3}} - \frac{d ^{2} y}{d x ^{2}} = 0

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

Solution steps

\frac{d ^{3} y}{d x ^{3}} - \frac{d ^{2} y}{d x ^{2}} = 0

Solve linear ODE:

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

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

y^{^{'''}} - y^{^{''}} + 25 y^{^{'}} - 25 y = 0

y^{^{''}} - 16 y^{^{'}} - 63 y = 0

y^{^{''}} + \frac{3}{2} y^{^{'}} + \frac{3}{8} y = 0

5 \frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} - 90 y = 0

y^{^{''}} - 9 y = 0, y^{^{'}} (0) = 0

What is the solution for (d^3y)/(dx^3)-(d^2y)/(dx^2)=0 ?
The solution for (d^3y)/(dx^3)-(d^2y)/(dx^2)=0 is y=c_{1}e^x+c_{2}+c_{3}x