Internal problem ID [3360]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 22
Problem number: 620.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational]
Solve \begin {gather*} \boxed {\left (a +b +x +y\right )^{2} y^{\prime }-2 \left (a +y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve((a+b+x+y(x))^2*diff(y(x),x) = 2*(a+y(x))^2,y(x), singsol=all)
\[ y \relax (x ) = -a -\tan \left (\RootOf \left (-2 \textit {\_Z} +\ln \left (\tan \left (\textit {\_Z} \right )\right )+\ln \left (b +x \right )+c_{1}\right )\right ) \left (b +x \right ) \]
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 25
DSolve[(a+b+x+y[x])^2 y'[x]==2(a+y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\log (a+y(x))-2 \text {ArcTan}\left (\frac {b+x}{a+y(x)}\right )=c_1,y(x)\right ] \]