Internal problem ID [5034]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 37.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (x +4 y\right ) y^{\prime }-2 x -3 y+5=0} \end {gather*}
✓ Solution by Maple
Time used: 0.953 (sec). Leaf size: 64
dsolve((x+4*y(x))*diff(y(x),x)=2*x+3*y(x)-5,y(x), singsol=all)
\[ y \relax (x ) = -1+\frac {\left (x -4\right ) \left (\RootOf \left (\textit {\_Z}^{36}+3 \left (x -4\right )^{6} c_{1} \textit {\_Z}^{6}-2 \left (x -4\right )^{6} c_{1}\right )^{6}-1\right )}{\RootOf \left (\textit {\_Z}^{36}+3 \left (x -4\right )^{6} c_{1} \textit {\_Z}^{6}-2 \left (x -4\right )^{6} c_{1}\right )^{6}} \]
✓ Solution by Mathematica
Time used: 60.07 (sec). Leaf size: 805
DSolve[(x+4*y[x])*y'[x]==2*x+3*y[x]-5,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{4}+\frac {1}{4 \text {Root}\left [\text {$\#$1}^6 \left (-3125 x^6+75000 x^5-750000 x^4+4000000 x^3-12000000 x^2+19200000 x-12800000+3125 e^{\frac {15 c_1}{8}}\right )+\text {$\#$1}^4 \left (1875 x^4-30000 x^3+180000 x^2-480000 x+480000\right )+\text {$\#$1}^3 \left (-1000 x^3+12000 x^2-48000 x+64000\right )+\text {$\#$1}^2 \left (225 x^2-1800 x+3600\right )+\text {$\#$1} (96-24 x)+1\&,1\right ]} \\ y(x)\to -\frac {x}{4}+\frac {1}{4 \text {Root}\left [\text {$\#$1}^6 \left (-3125 x^6+75000 x^5-750000 x^4+4000000 x^3-12000000 x^2+19200000 x-12800000+3125 e^{\frac {15 c_1}{8}}\right )+\text {$\#$1}^4 \left (1875 x^4-30000 x^3+180000 x^2-480000 x+480000\right )+\text {$\#$1}^3 \left (-1000 x^3+12000 x^2-48000 x+64000\right )+\text {$\#$1}^2 \left (225 x^2-1800 x+3600\right )+\text {$\#$1} (96-24 x)+1\&,2\right ]} \\ y(x)\to -\frac {x}{4}+\frac {1}{4 \text {Root}\left [\text {$\#$1}^6 \left (-3125 x^6+75000 x^5-750000 x^4+4000000 x^3-12000000 x^2+19200000 x-12800000+3125 e^{\frac {15 c_1}{8}}\right )+\text {$\#$1}^4 \left (1875 x^4-30000 x^3+180000 x^2-480000 x+480000\right )+\text {$\#$1}^3 \left (-1000 x^3+12000 x^2-48000 x+64000\right )+\text {$\#$1}^2 \left (225 x^2-1800 x+3600\right )+\text {$\#$1} (96-24 x)+1\&,3\right ]} \\ y(x)\to -\frac {x}{4}+\frac {1}{4 \text {Root}\left [\text {$\#$1}^6 \left (-3125 x^6+75000 x^5-750000 x^4+4000000 x^3-12000000 x^2+19200000 x-12800000+3125 e^{\frac {15 c_1}{8}}\right )+\text {$\#$1}^4 \left (1875 x^4-30000 x^3+180000 x^2-480000 x+480000\right )+\text {$\#$1}^3 \left (-1000 x^3+12000 x^2-48000 x+64000\right )+\text {$\#$1}^2 \left (225 x^2-1800 x+3600\right )+\text {$\#$1} (96-24 x)+1\&,4\right ]} \\ y(x)\to -\frac {x}{4}+\frac {1}{4 \text {Root}\left [\text {$\#$1}^6 \left (-3125 x^6+75000 x^5-750000 x^4+4000000 x^3-12000000 x^2+19200000 x-12800000+3125 e^{\frac {15 c_1}{8}}\right )+\text {$\#$1}^4 \left (1875 x^4-30000 x^3+180000 x^2-480000 x+480000\right )+\text {$\#$1}^3 \left (-1000 x^3+12000 x^2-48000 x+64000\right )+\text {$\#$1}^2 \left (225 x^2-1800 x+3600\right )+\text {$\#$1} (96-24 x)+1\&,5\right ]} \\ y(x)\to -\frac {x}{4}+\frac {1}{4 \text {Root}\left [\text {$\#$1}^6 \left (-3125 x^6+75000 x^5-750000 x^4+4000000 x^3-12000000 x^2+19200000 x-12800000+3125 e^{\frac {15 c_1}{8}}\right )+\text {$\#$1}^4 \left (1875 x^4-30000 x^3+180000 x^2-480000 x+480000\right )+\text {$\#$1}^3 \left (-1000 x^3+12000 x^2-48000 x+64000\right )+\text {$\#$1}^2 \left (225 x^2-1800 x+3600\right )+\text {$\#$1} (96-24 x)+1\&,6\right ]} \\ \end{align*}