Solve the following. $\large\frac{dy}{dx}+\frac{y}{x}$$\;=\;\sin(x^{2}) 1 Answer Toolbox: • Linear Differential equation. • This is of the form \large\frac{dy}{dx}$$+Py=Q$ where P and Q are functions of x only.
• The integrating factor $I= e^{\int \large pfd}$ and the $G.S$ is$ye^{\large pdx}=\int Q e^{\large pdx} dx+c$
Step 1:
$\large\frac{dy}{dx}+\frac{x}{y}$$=\sin (x^2) P(x)=\large\frac{1}{x}$$, Q(x)= \sin (x^2)$
$e^{\large\int pdx}= e^{\int \large\frac{1}{x}}$$dx \qquad= e^{\large\log x} \qquad=x The solution is yx= \int \sin (x^2) .x dx+c yx=\large\frac{-1}{2}$$\cos x^2+c$

answered Sep 6, 2013 by
edited Sep 6, 2013 by meena.p