60.1.41 problem 41

Internal problem ID [10055]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 41
Date solved : Monday, January 27, 2025 at 06:19:56 PM
CAS classification : [[_homogeneous, `class G`], _Abel]

\begin{align*} y^{\prime }+a x y^{3}+b y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.082 (sec). Leaf size: 103

dsolve(diff(y(x),x) + a*x*y(x)^3 + b*y(x)^2=0,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{\operatorname {RootOf}\left (2 \sqrt {b^{2}+4 a}\, b \,\operatorname {arctanh}\left (\frac {2 a \,{\mathrm e}^{\textit {\_Z}}+b}{\sqrt {b^{2}+4 a}}\right )-\ln \left (x^{2} \left (a \,{\mathrm e}^{2 \textit {\_Z}}+b \,{\mathrm e}^{\textit {\_Z}}-1\right )\right ) b^{2}+2 c_{1} b^{2}+2 \textit {\_Z} \,b^{2}-4 \ln \left (x^{2} \left (a \,{\mathrm e}^{2 \textit {\_Z}}+b \,{\mathrm e}^{\textit {\_Z}}-1\right )\right ) a +8 c_{1} a +8 a \textit {\_Z} \right )}}{x} \]

✓ Solution by Mathematica

Time used: 0.198 (sec). Leaf size: 103

DSolve[D[y[x],x] + a*x*y[x]^3 + b*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\frac {b^2 \left (\frac {2 \arctan \left (\frac {-2 a x y(x)-b}{b \sqrt {-\frac {4 a}{b^2}-1}}\right )}{\sqrt {-\frac {4 a}{b^2}-1}}-\log \left (\frac {a (-x) y(x) (-a x y(x)-b)-a}{a^2 x^2 y(x)^2}\right )\right )}{2 a}=-\frac {b^2 \log (x)}{a}+c_1,y(x)\right ] \]