Solution of the differential equation $(x^{2} + y^{3}) (2 x^{2} d x + 3 y d y) = 12 x d x + 18 y^{2} d y$ is

\frac{2}{3} x^{3} + \frac{3}{2} y^{2} = 6 l n (x^{2} + y^{3}) + c

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x^{2} + y^{3} = 9 l n (x^{2} + y^{3}) + c

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\frac{2}{3} x^{3} + \frac{3}{2} y^{2} = 6 l n (x^{3} + y^{2}) + c

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x^{3} + y^{2} = 6 l n (x^{2} + y^{3}) + c

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Solution

The correct option is B $\frac{2}{3} x^{3} + \frac{3}{2} y^{2} = 6 l n (x^{2} + y^{3}) + c$
$L H S ⟶ (x^{2} + y^{3}) (2 x^{2} d x + 3 y d y) = 2 x^{4} d x + 3 x^{2} y d y + 2 x^{2} y^{3} d x + 3 y^{4} d y \Rightarrow 2 x^{4} d x + 3 x^{2} y d y + 2 x^{2} y^{3} d x + 3 y^{4} d y = 12 x d x + 18 y^{2} d y (o r) t h e g i v e n q u e s t i o n c a n b e w r i t t e n a s (2 x^{2} d x + 3 y d y) = \frac{6 (2 x d x + 3 y^{2} d y)}{x^{2} + y^{3}} i n t e g r a t i n g \Rightarrow \frac{2}{3} x^{3} + \frac{3}{2} y^{2} = 6 l n (x^{2} + y^{3}) + C$

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Solution of the differential equation (x2+y3)(2x2dx+3ydy)=12x dx+18y2dy is

The correct option is B 23x3+32y2=6ln(x2+y3)+cLHS⟶(x2+y3)(2x2dx+3ydy)=2x4dx+3x2ydy+2x2y3dx+3y4dy⇒2x4dx+3x2ydy+2x2y3dx+3y4dy=12xdx+18y2dy(or)thegivenquestioncanbewrittenas(2x2dx+3ydy)=6(2xdx+3y2dy)x2+y3integrating⇒23x3+32y2=6ln(x2+y3)+C

Solution of the differential equation $(x^{2} + y^{3}) (2 x^{2} d x + 3 y d y) = 12 x d x + 18 y^{2} d y$ is