CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsDifferential Equations and Modeling3 Marks
Question
Solve : $\left(x^2-y x^2\right) d y+\left(y^2+x y^2\right) d x=0$
✓
Answer
Given, $\left(x^2-y x^2\right) d y+\left(y^2+x y^2\right) d x=0$ $\Rightarrow \quad x^2(1-y) d y+y^2(1+x) d x=0$ $\Rightarrow \quad \frac{1-y}{y^2} d y+\frac{1+x}{x^2} d x=0$ On integration, we get $\int \frac{1-y}{y^2} d y+\int \frac{1+x}{x^2} d x=0$ $\Rightarrow \int \frac{1}{y^2} d y-\int \frac{1}{y} d y+\int \frac{1}{x^2} d x+\int \frac{1}{x} d x=0$ $\Rightarrow \quad \log \left(\frac{x}{y}\right)-\frac{1}{x}-\frac{1}{y}= C$ $\Rightarrow \quad \log \left(\frac{x}{y}\right)=C+\frac{1}{x}+\frac{1}{y}$
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