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The solution of $y (2 x^{2} y + e^{x}) d x - (e^{x} + y^{3}) d y = 0$ , if $y (0) = 1$ is

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6ex+4x3y−3y3−3y=0

y2ex−4xy−3x3−3=0

x3ex−4x3y−3xy3−3x=0

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detailed solution

Correct option is A

yexdx−exdy+2x2y2dx−y3dy=0⇒yexdx−exdyy2+2x2dx−ydy=0dexy+2x2dx−ydy=0 Integrating we get, exy+2x33−y22=Cy(0)=1⇒1+0−12=C given C=12∴exy+2x33−y22=12 Gives 6ex+4x3y−3y3−3y=0

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The solution of y2x2y+exdx−ex+y3dy=0, if y0=1 is

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The solution of $y (2 x^{2} y + e^{x}) d x - (e^{x} + y^{3}) d y = 0$ , if $y (0) = 1$ is