Question

Determine whether the following DE is seperable, linear , exact, homogeneous, and Bernoulli. next find its solutions by respective methods.

(1+2y^2)dy = ycosxdx

Answer 1

Rewrite in the form of a first order separable ODE

$$\dfrac{1+2y^2}{y}dy=\cos xdx$$

Integrate

$$\int\dfrac{1+2y^2}{y}dy=\int\cos xdx$$

$$\ln (|y|)+y^2=\sin x+C$$