What is the solution for 4(dy)/(dx)-3(d^2y)/(dx^2)=0 ?

The solution for 4(dy)/(dx)-3(d^2y)/(dx^2)=0 is y=c_{1}+c_{2}e^{(4x)/3}

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'''}} + 5 y^{^{''}} - 11 y^{^{'}} - 39 y = 0

4 y^{^{''}} + 12 y^{^{'}} + 9 y = 0, y (0) = 3, y^{^{'}} (0) = 5

y^{^{''''}} + 5 y^{^{''}} - 36 y = 0

y^{^{''}} + 16 y = 0, y (\frac{π}{8}) = - 2, y^{^{'}} (\frac{π}{8}) = 16

y^{^{'''}} + 2 y^{^{''}} - 15 y^{^{'}} - 36 y = 0

What is the solution for 4(dy)/(dx)-3(d^2y)/(dx^2)=0 ?
The solution for 4(dy)/(dx)-3(d^2y)/(dx^2)=0 is y=c_{1}+c_{2}e^{(4x)/3}