29.2.17 problem 42

Internal problem ID [4650]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 42
Date solved : Monday, January 27, 2025 at 09:29:24 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.596 (sec). Leaf size: 14

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

\[ y(x)\to -x+\tan (x+c_1) \]