Question

Solve for the linear equation Dm/dn + m/n = n^2

Answer 1

SOLUTION

TO SOLVE

The differential equation

$\displaystyle \sf{ \frac{dm}{dn} + \frac{m}{n} = {n}^{2} }$

EVALUATION

Here the given differential equation is

$\displaystyle \sf{ \frac{dm}{dn} + \frac{m}{n} = {n}^{2} }$

Integrating factor = I.F

$\displaystyle \sf{ = {e}^{ \int \frac{1}{n} dn} }$

$\displaystyle \sf{ = {e}^{ \log n} }$

$\displaystyle \sf{ = n }$

So the required solution is obtained by

$\displaystyle \sf{ y.n = \int \: {n}^{2}.n \: dn }$

$\displaystyle \sf{ \implies \: yn = \int \: {n}^{3}\: dn }$

$\displaystyle \sf{ \implies \: yn = \frac{ {n}^{3 + 1} }{3 + 1} + c }$

$\displaystyle \sf{ \implies \: yn = \frac{ {n}^{4} }{4} + c }$

Where C is constant

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