I have the differential equation

${x}^{2}{y}^{\prime}(x)+2xy(x)={y}^{2}(x)$

With initial condition y(1)=1 and I want to solve this, by observation, we can see the LHS is ${x}^{2}y(x)$ but I am unfamiliar with tackling the RHS and was wondering where to go from here.

${x}^{2}y(x)=\int {y}^{2}(x)\text{}dx$

${x}^{2}{y}^{\prime}(x)+2xy(x)={y}^{2}(x)$

With initial condition y(1)=1 and I want to solve this, by observation, we can see the LHS is ${x}^{2}y(x)$ but I am unfamiliar with tackling the RHS and was wondering where to go from here.

${x}^{2}y(x)=\int {y}^{2}(x)\text{}dx$