What is the solution for (d^2y)/(dx^2)-7(dy)/(dx)+12y=0 ?

The solution for (d^2y)/(dx^2)-7(dy)/(dx)+12y=0 is y=c_{1}e^{4x}+c_{2}e^{3x}

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(d^2y)/(dx^2)-7(dy)/(dx)+12y=0

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} + 12 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} + 12 y = 0

Solve linear ODE:

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

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

\int \frac{( x ^{3} - 5 x + 2 )}{x ^{\frac{1}{2}}} d x

\frac{d}{d x} ((4 x^{2} + 3 x)^{2})

\int x^{3} x^{2} + 34 d x

x \to 4 + lim (- \frac{3}{8 - 2 x})

x \to 0 lim (∣ x ∣ sin (x))

What is the solution for (d^2y)/(dx^2)-7(dy)/(dx)+12y=0 ?
The solution for (d^2y)/(dx^2)-7(dy)/(dx)+12y=0 is y=c_{1}e^{4x}+c_{2}e^{3x}