Solving 2nd Order Differential Equations

Category: Differential Equations, Integral Calculus

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Find the general solution for

Solution:

Consider the given equation above

The given equation is a 2nd Order Differential Equation because the second derivative of y with respect to x is involved. We can rewrite given equation as follows

Multiply both sides of the equation by dx, we have

Integrate on both sides of the equation, we have

Multiply both sides of the equation by dx, we have

Integrate on both sides of the equation, we have

but

Hence, the above equation becomes

where B = C₁ - 1.Therefore, the general solution is