29.3.5 problem 59

Internal problem ID [4667]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 3
Problem number : 59
Date solved : Monday, January 27, 2025 at 09:30:49 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 44

dsolve(diff(y(x),x) = a0+a1*y(x)+a2*y(x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-\operatorname {a1} +\tan \left (\frac {\sqrt {4 \operatorname {a0} \operatorname {a2} -\operatorname {a1}^{2}}\, \left (x +c_{1} \right )}{2}\right ) \sqrt {4 \operatorname {a0} \operatorname {a2} -\operatorname {a1}^{2}}}{2 \operatorname {a2}} \]

✓ Solution by Mathematica

Time used: 47.053 (sec). Leaf size: 106

DSolve[D[y[x],x]==a0+a1 y[x]+ a2 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {-\text {a1}+\sqrt {4 \text {a0} \text {a2}-\text {a1}^2} \tan \left (\frac {1}{2} (x+c_1) \sqrt {4 \text {a0} \text {a2}-\text {a1}^2}\right )}{2 \text {a2}} \\ y(x)\to \frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}-\text {a1}}{2 \text {a2}} \\ y(x)\to -\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}+\text {a1}}{2 \text {a2}} \\ \end{align*}