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प्रश्न
For the differential equation, find the general solution:
`dy/dx + y/x = x^2`
उत्तर
This is a linear differential equation of the form `dy/dx + y/x` + Py = Q.
Here P = `1/x` and Q = x2
∴ I.F. = `e^(int P dx) = e^(int 1/x dx) = e^(log x) = x`
Hence, the general solution of the differential equation
`y × I.F. = int Q xx I.F. dx + C`
`y * x = int x^2 * x + C`
xy = `int x^3 + C`
xy = `x^4/4 + C`
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