56.1.36 problem 37

Internal problem ID [8748]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 37
Date solved : Monday, January 27, 2025 at 04:46:20 PM
CAS classification : [_rational, _Riccati]

\begin{align*} x y^{\prime }-2 y+b y^{2}&=c \,x^{4} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

dsolve(x*diff(y(x),x)-2*y(x)+b*y(x)^2=c*x^4,y(x), singsol=all)
 

\[ y = \frac {i \tan \left (-\frac {i x^{2} \sqrt {b}\, \sqrt {c}}{2}+c_{1} \right ) x^{2} \sqrt {c}}{\sqrt {b}} \]

✓ Solution by Mathematica

Time used: 0.242 (sec). Leaf size: 153

DSolve[x*D[y[x],x]-2*y[x]+b*y[x]^2==c*x^4,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\sqrt {c} x^2 \left (-\cos \left (\frac {1}{2} \sqrt {-b} \sqrt {c} x^2\right )+c_1 \sin \left (\frac {1}{2} \sqrt {-b} \sqrt {c} x^2\right )\right )}{\sqrt {-b} \left (\sin \left (\frac {1}{2} \sqrt {-b} \sqrt {c} x^2\right )+c_1 \cos \left (\frac {1}{2} \sqrt {-b} \sqrt {c} x^2\right )\right )} \\ y(x)\to \frac {\sqrt {c} x^2 \tan \left (\frac {1}{2} \sqrt {-b} \sqrt {c} x^2\right )}{\sqrt {-b}} \\ \end{align*}