2.17 problem 42

Internal problem ID [2797]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 2
Problem number: 42.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class C], _Riccati]

Solve \begin {gather*} \boxed {y^{\prime }-\left (x +y\right )^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 16

dsolve(diff(y(x),x) = (x+y(x))^2,y(x), singsol=all)
 

\[ y \relax (x ) = -x -\tan \left (-x +c_{1}\right ) \]

Solution by Mathematica

Time used: 0.585 (sec). Leaf size: 14

DSolve[y'[x]==(x+y[x])^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x+\tan (x+c_1) \\ \end{align*}