Internal problem ID [14368]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {-7 t y+5 y^{2}+t y y^{\prime }=-2 t^{2}} \]
✓ Solution by Maple
Time used: 1.031 (sec). Leaf size: 52
dsolve((2*t^2-7*t*y(t)+5*y(t)^2)+(t*y(t))*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \frac {t \left (-2 c_{1} t^{2}+\operatorname {RootOf}\left (\textit {\_Z}^{4}-3 c_{1} t^{2}+2 \textit {\_Z} \right )\right )}{-3 c_{1} t^{2}+2 \operatorname {RootOf}\left (\textit {\_Z}^{4}-3 c_{1} t^{2}+2 \textit {\_Z} \right )} \]
✓ Solution by Mathematica
Time used: 60.175 (sec). Leaf size: 1935
DSolve[(2*t^2-7*t*y[t]+5*y[t]^2)+(t*y[t])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {-108 t^6+t^5 \sqrt {\frac {54 e^{6 c_1} t^6 \left (-4+\frac {3\ 2^{2/3} t^7}{\sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}}\right )+81 \sqrt [3]{2} t^5 \sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}+16 e^{12 c_1}}{t^{10}}}+t^5 \sqrt {\frac {1296 t^{11} \left (-18 t^6+e^{6 c_1}\right )+32 t^5 \left (-27 t^6+e^{6 c_1}\right ){}^2-\frac {162\ 2^{2/3} e^{6 c_1} t^{18}}{\sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}}-81 \sqrt [3]{2} t^{10} \sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}+\frac {4 e^{6 c_1} \left (2187 t^{12}-648 e^{6 c_1} t^6+32 e^{12 c_1}\right )}{\sqrt {\frac {54 e^{6 c_1} t^6 \left (-4+\frac {3\ 2^{2/3} t^7}{\sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}}\right )+81 \sqrt [3]{2} t^5 \sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}+16 e^{12 c_1}}{t^{10}}}}}{t^{15}}}+4 e^{6 c_1}}{162 t^5} \\ y(t)\to \frac {108 t^6-t^5 \sqrt {\frac {54 e^{6 c_1} t^6 \left (-4+\frac {3\ 2^{2/3} t^7}{\sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}}\right )+81 \sqrt [3]{2} t^5 \sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}+16 e^{12 c_1}}{t^{10}}}+t^5 \sqrt {\frac {1296 t^{11} \left (-18 t^6+e^{6 c_1}\right )+32 t^5 \left (-27 t^6+e^{6 c_1}\right ){}^2-\frac {162\ 2^{2/3} e^{6 c_1} t^{18}}{\sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}}-81 \sqrt [3]{2} t^{10} \sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}+\frac {4 e^{6 c_1} \left (2187 t^{12}-648 e^{6 c_1} t^6+32 e^{12 c_1}\right )}{\sqrt {\frac {54 e^{6 c_1} t^6 \left (-4+\frac {3\ 2^{2/3} t^7}{\sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}}\right )+81 \sqrt [3]{2} t^5 \sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}+16 e^{12 c_1}}{t^{10}}}}}{t^{15}}}-4 e^{6 c_1}}{162 t^5} \\ y(t)\to \frac {108 t^6+t^5 \sqrt {\frac {54 e^{6 c_1} t^6 \left (-4+\frac {3\ 2^{2/3} t^7}{\sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}}\right )+81 \sqrt [3]{2} t^5 \sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}+16 e^{12 c_1}}{t^{10}}}-t^5 \sqrt {\frac {1296 t^{11} \left (-18 t^6+e^{6 c_1}\right )+32 t^5 \left (-27 t^6+e^{6 c_1}\right ){}^2-\frac {162\ 2^{2/3} e^{6 c_1} t^{18}}{\sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}}-81 \sqrt [3]{2} t^{10} \sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}-\frac {4 e^{6 c_1} \left (2187 t^{12}-648 e^{6 c_1} t^6+32 e^{12 c_1}\right )}{\sqrt {\frac {54 e^{6 c_1} t^6 \left (-4+\frac {3\ 2^{2/3} t^7}{\sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}}\right )+81 \sqrt [3]{2} t^5 \sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}+16 e^{12 c_1}}{t^{10}}}}}{t^{15}}}-4 e^{6 c_1}}{162 t^5} \\ y(t)\to \frac {108 t^6+t^5 \sqrt {\frac {54 e^{6 c_1} t^6 \left (-4+\frac {3\ 2^{2/3} t^7}{\sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}}\right )+81 \sqrt [3]{2} t^5 \sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}+16 e^{12 c_1}}{t^{10}}}+t^5 \sqrt {\frac {1296 t^{11} \left (-18 t^6+e^{6 c_1}\right )+32 t^5 \left (-27 t^6+e^{6 c_1}\right ){}^2-\frac {162\ 2^{2/3} e^{6 c_1} t^{18}}{\sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}}-81 \sqrt [3]{2} t^{10} \sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}-\frac {4 e^{6 c_1} \left (2187 t^{12}-648 e^{6 c_1} t^6+32 e^{12 c_1}\right )}{\sqrt {\frac {54 e^{6 c_1} t^6 \left (-4+\frac {3\ 2^{2/3} t^7}{\sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}}\right )+81 \sqrt [3]{2} t^5 \sqrt [3]{e^{12 c_1} t^9+\sqrt {e^{18 c_1} t^{18} \left (-16 t^6+e^{6 c_1}\right )}}+16 e^{12 c_1}}{t^{10}}}}}{t^{15}}}-4 e^{6 c_1}}{162 t^5} \\ \end{align*}