60.1.38 problem 38

Internal problem ID [10052]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 38
Date solved : Monday, January 27, 2025 at 06:19:44 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Abel]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 34

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

\[ y = \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} +2 \left (\int _{}^{\textit {\_Z}}\frac {1}{2 a \,\textit {\_a}^{3}+\textit {\_a} +2 b}d \textit {\_a} \right )\right )}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.163 (sec). Leaf size: 75

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

\[ \text {Solve}\left [\int _1^{\sqrt [3]{\frac {a x^{3/2}}{b}} y(x)}\frac {1}{K[1]^3-\frac {1}{2} \sqrt [3]{-\frac {1}{a b^2}} K[1]+1}dK[1]=\frac {a x \log (x)}{\left (\frac {a x^{3/2}}{b}\right )^{2/3}}+c_1,y(x)\right ] \]