64.5.36 problem 40

Internal problem ID [13349]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 40
Date solved : Tuesday, January 28, 2025 at 05:31:24 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=-y^{2}+y x +1 \end{align*}

✓ Solution by Maple

Time used: 0.063 (sec). Leaf size: 53

dsolve(diff(y(x),x)=-y(x)^2+x*y(x)+1,y(x), singsol=all)
 

\[ y = \frac {\sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, x}{2}\right ) x +2 c_{1} x +2 \,{\mathrm e}^{-\frac {x^{2}}{2}}}{\sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, x}{2}\right )+2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.147 (sec). Leaf size: 45

DSolve[D[y[x],x]==-y[x]^2+x*y[x]+1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x+\frac {e^{-\frac {x^2}{2}}}{\sqrt {\frac {\pi }{2}} \text {erf}\left (\frac {x}{\sqrt {2}}\right )+c_1} \\ y(x)\to x \\ \end{align*}