Internal problem ID [5782]
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: 32.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }+\frac {4 x +3 y+15}{2 x +y+7}=0} \]
✓ Solution by Maple
Time used: 1.234 (sec). Leaf size: 227
dsolve(diff(y(x),x)=-(4*x+3*y(x)+15)/(2*x+y(x)+7),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-24 \left (x +3\right )^{2} c_{1} \left (x +\frac {10}{3}\right ) {\left (4 \sqrt {-4 \left (-\frac {1}{4}+\left (x +3\right )^{3} c_{1} \right ) \left (x +3\right )^{6} c_{1}^{2}}+4 \left (x^{3}+9 x^{2}+27 x +27\right ) c_{1} \right )}^{\frac {2}{3}}+i \left (-16 \left (x +3\right )^{6} c_{1}^{2}+\left (4 c_{1} x^{3}+36 c_{1} x^{2}+108 c_{1} x +4 \sqrt {-4 \left (-\frac {1}{4}+\left (x +3\right )^{3} c_{1} \right ) \left (x +3\right )^{6} c_{1}^{2}}+108 c_{1} \right )^{\frac {4}{3}}\right ) \sqrt {3}+16 \left (x +3\right )^{6} c_{1}^{2}+\left (4 c_{1} x^{3}+36 c_{1} x^{2}+108 c_{1} x +4 \sqrt {-4 \left (-\frac {1}{4}+\left (x +3\right )^{3} c_{1} \right ) \left (x +3\right )^{6} c_{1}^{2}}+108 c_{1} \right )^{\frac {4}{3}}}{8 {\left (4 \sqrt {-4 \left (-\frac {1}{4}+\left (x +3\right )^{3} c_{1} \right ) \left (x +3\right )^{6} c_{1}^{2}}+4 \left (x^{3}+9 x^{2}+27 x +27\right ) c_{1} \right )}^{\frac {2}{3}} \left (x +3\right )^{2} c_{1}} \]
✓ Solution by Mathematica
Time used: 60.066 (sec). Leaf size: 763
DSolve[y'[x]==-(4*x+3*y[x]+15)/(2*x+y[x]+7),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^6+288 x^5+2160 x^4+8640 x^3+19440 x^2+23328 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-24 x^4-288 x^3-1296 x^2-2592 x-1944\right )+\text {$\#$1}^3 \left (-8 x^3-72 x^2-216 x-216\right )+\text {$\#$1}^2 \left (9 x^2+54 x+81\right )+\text {$\#$1} (6 x+18)+1\&,1\right ]}-2 x-7 \\ y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^6+288 x^5+2160 x^4+8640 x^3+19440 x^2+23328 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-24 x^4-288 x^3-1296 x^2-2592 x-1944\right )+\text {$\#$1}^3 \left (-8 x^3-72 x^2-216 x-216\right )+\text {$\#$1}^2 \left (9 x^2+54 x+81\right )+\text {$\#$1} (6 x+18)+1\&,2\right ]}-2 x-7 \\ y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^6+288 x^5+2160 x^4+8640 x^3+19440 x^2+23328 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-24 x^4-288 x^3-1296 x^2-2592 x-1944\right )+\text {$\#$1}^3 \left (-8 x^3-72 x^2-216 x-216\right )+\text {$\#$1}^2 \left (9 x^2+54 x+81\right )+\text {$\#$1} (6 x+18)+1\&,3\right ]}-2 x-7 \\ y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^6+288 x^5+2160 x^4+8640 x^3+19440 x^2+23328 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-24 x^4-288 x^3-1296 x^2-2592 x-1944\right )+\text {$\#$1}^3 \left (-8 x^3-72 x^2-216 x-216\right )+\text {$\#$1}^2 \left (9 x^2+54 x+81\right )+\text {$\#$1} (6 x+18)+1\&,4\right ]}-2 x-7 \\ y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^6+288 x^5+2160 x^4+8640 x^3+19440 x^2+23328 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-24 x^4-288 x^3-1296 x^2-2592 x-1944\right )+\text {$\#$1}^3 \left (-8 x^3-72 x^2-216 x-216\right )+\text {$\#$1}^2 \left (9 x^2+54 x+81\right )+\text {$\#$1} (6 x+18)+1\&,5\right ]}-2 x-7 \\ y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^6+288 x^5+2160 x^4+8640 x^3+19440 x^2+23328 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-24 x^4-288 x^3-1296 x^2-2592 x-1944\right )+\text {$\#$1}^3 \left (-8 x^3-72 x^2-216 x-216\right )+\text {$\#$1}^2 \left (9 x^2+54 x+81\right )+\text {$\#$1} (6 x+18)+1\&,6\right ]}-2 x-7 \\ \end{align*}