Internal problem ID [8259]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 679.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y+\ln \relax (x ) x^{3}+x^{4}+x^{3}+7 x y^{2} \ln \relax (x )+7 y^{2} x^{2}+7 x y^{2}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 37
dsolve(diff(y(x),x) = (y(x)+x^3*ln(x)+x^4+x^3+7*x*y(x)^2*ln(x)+7*x^2*y(x)^2+7*x*y(x)^2)/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\frac {\left (6 x^{2} \ln \relax (x )+4 x^{3}+3 x^{2}+12 c_{1}\right ) \sqrt {7}}{12}\right ) x \sqrt {7}}{7} \]
✓ Solution by Mathematica
Time used: 0.513 (sec). Leaf size: 43
DSolve[y'[x] == (x^3 + x^4 + x^3*Log[x] + y[x] + 7*x*y[x]^2 + 7*x^2*y[x]^2 + 7*x*Log[x]*y[x]^2)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \tan \left (\frac {1}{12} \sqrt {7} \left ((4 x+3) x^2+6 x^2 \log (x)+12 c_1\right )\right )}{\sqrt {7}} \\ \end{align*}