60.1.279 problem 280

Internal problem ID [10293]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 280
Date solved : Monday, January 27, 2025 at 06:50:46 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 24

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

\[ y = a \operatorname {RootOf}\left (\tan \left (\textit {\_Z} \right ) a -a \textit {\_Z} +c_{1} -x \right )-c_{1} \]

✓ Solution by Mathematica

Time used: 0.175 (sec). Leaf size: 114

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (-\frac {a^2}{a^2+x^2+K[2]^2+2 x K[2]}-\int _1^x\frac {a^2 (2 K[1]+2 K[2])}{\left (a^2+K[1]^2+K[2]^2+2 K[1] K[2]\right )^2}dK[1]+1\right )dK[2]+\int _1^x-\frac {a^2}{a^2+K[1]^2+y(x)^2+2 K[1] y(x)}dK[1]=c_1,y(x)\right ] \]