Solution of differential equati x d y-d x-y-ex y-1 n x2x d y-d x-yA- y-x-e-x y-cB- -x-e-x y-cC- x-y-e-x y-cD- - x - y - e - xy - c

The correct option is B y/x + e^ xy = c(x dy/dx + y) = e^xy 1n x^2 (x dy/dx y) (x dy/dx + y) = e^xy 1n x^2(x dy/dx y)= e^xy/x^2(x dy/dx y) e^ xy(xd ...

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Standard XII

Mathematics

Solving Homogeneous Differential Equations

Solution of d...

Question

Solution of differential equation
$(x \frac{d y}{d x} + y) = e^{x y - 1 n x^{2}} (x \frac{d y}{d x} - y)$

\frac{y}{x} - e^{- x y} = c

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\frac{x}{y} + e^{- x y} = c

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\frac{y}{x} + e^{- x y} = c

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\frac{- x}{y} - e^{- x y} = c

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Solution

The correct option is C $\frac{y}{x} + e^{- x y} = c$
$(x \frac{d y}{d x} + y) = e^{x y - 1 n x^{2}} (x \frac{d y}{d x} - y) (x \frac{d y}{d x} + y) = e^{x y - 1 n x^{2}} (x \frac{d y}{d x} - y) = \frac{e^{x y}}{x^{2}} (x \frac{d y}{d x} - y) e^{- x y} (x d y + y d x) = \frac{x d y - y d x}{x^{2}} \Rightarrow - e^{x y} - \frac{y}{x} + c \Rightarrow \frac{y}{x} + e^{- x y} = c$

Suggest Corrections

Solution of differential equation (xdydx+y)=exy−1n x2(xdydx−y)

The correct option is C yx+e−xy=c(xdydx+y)=exy−1nx2(xdydx−y)(xdydx+y)=exy−1nx2(xdydx−y)=exyx2(xdydx−y)e−xy(xdy+ydx)=xdy−ydxx2⇒−exy−yx+c⇒yx+e−xy=c

Solution of differential equation
$(x \frac{d y}{d x} + y) = e^{x y - 1 n x^{2}} (x \frac{d y}{d x} - y)$