Internal problem ID [8012]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 432.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {\left (y^{\prime } x +a \right )^{2}-2 a y+x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.2 (sec). Leaf size: 615
dsolve((x*diff(y(x),x)+a)^2-2*a*y(x)+x^2 = 0,y(x), singsol=all)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 1.044 (sec). Leaf size: 81
DSolve[x^2 - 2*a*y[x] + (a + x*y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{y(x)=\frac {2 a x K[1]+x^2 K[1]^2+a^2+x^2}{2 a},x=-\frac {a \tanh ^{-1}\left (\frac {K[1]}{\sqrt {K[1]^2+1}}\right )}{\sqrt {K[1]^2+1}}+\frac {c_1}{\sqrt {K[1]^2+1}}\right \},\{y(x),K[1]\}\right ] \]