I an concerned about you saying "I know solution method for solving differentialequations". One of the first things you should have learned is that there is NO one method of solving differential equations
In particularly, this is a badly non-linear equation and there is no "method" for solving it. There are a number of ways of either getting an approximate solution or getting qualitative information about the solution.
1) Linearization. The set up of your equation implies that you are taking "0" as the bottom of the swing. As long as you do not swing the pendulum "too hard" you have the angle staying small and you can approximate sin(x) by x. Solve \theta''+ \theta=0.
2) "Quadrature". By the chain rule, if we let \omega= d\theta/dt,
\frac{d^2\theta}{dt^2}= \frac{d\omega}{dt}= \frac{d\omega}{d\theta}\frac{d\theta}{dt}= \omega\frac{d\omega}{dt}
The equation becomes
\omega\frac{d\omega}{d\theta}+ (g/l)sin(\theta)= 0
which is a separable first order equation for \omega. Of course, after solving for \omega you have another first order equation for \theta. That equation can be reduced to an integral but, an "elliptic integral, one that has no elementary anti-derivative. That means that it must be done numerically which is why this is an approximation method.
3) "perturbation". sin(\theta)= \theta- (1/3!)\theta^3+ (1/5!)\theta^5- .... Dropping all except the \theta gives the linear equation of (1). Then subtract that solution from \theta and put the difference into the equation including the \theta^2 term. Continue as long as you wish.
4) "phase plane". Go ahead and integrate \int d\omega= -(g/l)sin(\theta)d\theta to get \omega= (g/l)cos(\theta)+ C and graph \omega against \theta for different values of C. That gives information about the behavior of solutions.
