75.4.16 problem 61

Internal problem ID [16718]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 61
Date solved : Tuesday, January 28, 2025 at 09:19:26 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.097 (sec). Leaf size: 24

dsolve((x+y(x))^2*diff(y(x),x)=a^2,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: 0.172 (sec). Leaf size: 114

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

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