60.1.19 problem 19

Internal problem ID [10033]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 19
Date solved : Monday, January 27, 2025 at 06:18:54 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }-\left (x +y\right )^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 16

dsolve(diff(y(x),x) - (y(x) + x)^2=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.534 (sec). Leaf size: 14

DSolve[D[y[x],x] - (y[x] + x)^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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