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# Solution - Solve the following differential equation: (x^2-1)dy/dx+2xy=2/(x^2-1) - CBSE (Commerce) Class 12 - Mathematics

ConceptSolutions of Linear Differential Equation

#### Question

Solve the following differential equation: (x^2-1)dy/dx+2xy=2/(x^2-1)

#### Solution

we have:

dy/dx+2x/(x^2-1)y=2/(x^2-1)^2

This is a linear differential equation of the form dy/dx+Py=Q ,where P=(2x)/(x^2-1) and Q=2/(x^2-1)^2

I.f=e^(intPdx)=e^(int(2x)/(x^2-1)dx)=e^(log(x^2-1))=(x^2-1)

Hence, the solution of the differential equation is given by

y.(x^2−1)=∫2/(x^2−1)^2×x(x2−1) dx + C

y.(x^2−1)=∫2/(x^2−1) dx + C

We know that,

∫dx/(x^2−a^2)=1/(2a)log∣(x−1)/(x+1)∣

y.(x^2−1)=2xx1/2log∣(x−1)/(x+1)∣+C

Is there an error in this question or solution?

#### Reference Material

Solution for question: Solve the following differential equation: (x^2-1)dy/dx+2xy=2/(x^2-1) concept: Solutions of Linear Differential Equation. For the courses CBSE (Commerce), CBSE (Science), CBSE (Arts), PUC Karnataka Science
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