60.1.36 problem 36

Internal problem ID [10050]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 36
Date solved : Tuesday, January 28, 2025 at 04:15:28 PM
CAS classification : [_Abel]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 71

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

\[ y = \frac {2 a}{a^{2} x^{2}+2 \operatorname {RootOf}\left (\operatorname {AiryBi}\left (\textit {\_Z} \right ) 2^{{1}/{3}} \left (-a^{2}\right )^{{1}/{3}} c_{1} x +2^{{1}/{3}} \left (-a^{2}\right )^{{1}/{3}} x \operatorname {AiryAi}\left (\textit {\_Z} \right )+2 \operatorname {AiryBi}\left (1, \textit {\_Z}\right ) c_{1} +2 \operatorname {AiryAi}\left (1, \textit {\_Z}\right )\right ) 2^{{1}/{3}} \left (-a^{2}\right )^{{1}/{3}}} \]

✓ Solution by Mathematica

Time used: 0.225 (sec). Leaf size: 195

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

\[ \text {Solve}\left [\frac {\operatorname {AiryAiPrime}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )-\left (-\frac {1}{2}\right )^{2/3} a^{2/3} x \operatorname {AiryAi}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )}{\operatorname {AiryBiPrime}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )-\left (-\frac {1}{2}\right )^{2/3} a^{2/3} x \operatorname {AiryBi}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )}+c_1=0,y(x)\right ] \]