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Show that the differential equation (x-y) …

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Show that the differential equation (x-y) dy/dx =x+2y is homogeneous and solve it

Posted by Moksh Sharma 7 years, 3 months ago

CBSE > Class 12 > Mathematics

1 answers

Ritik Yadav 7 years, 3 months ago

dy/dx= (x+2y)/(x-y) Since the degree of numerator and denominator is same,i.e. 1, then Let y=vx So dy/dx= v + x dy/dx (x+2vx)/(x-vx) = v+x dv/dx (1+2v)/(1-v) = v + x dv/dx (1+2v)/(1-v) - v = x dv/dx (1+2v-v+v^2 ) /(1-v) = x dv/dx (v^2 + v +1)/(1-v) =x dv/dx (1-v) dv/( v^2 +v+1) = dx/x So. Now you can integrate both sides and find the result...

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