Internal problem ID [4587]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y-3 x +\left (4 y+3 x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.357 (sec). Leaf size: 278
dsolve(y(x)-3*x+(4*y(x)+3*x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {3 x^{8} c_{1} \RootOf \left (\textit {\_Z}^{64} c_{1} x^{8}+12 \textit {\_Z}^{56} c_{1} x^{8}+48 \textit {\_Z}^{48} c_{1} x^{8}+64 \textit {\_Z}^{40} c_{1} x^{8}-1\right )^{56}+24 x^{8} c_{1} \RootOf \left (\textit {\_Z}^{64} c_{1} x^{8}+12 \textit {\_Z}^{56} c_{1} x^{8}+48 \textit {\_Z}^{48} c_{1} x^{8}+64 \textit {\_Z}^{40} c_{1} x^{8}-1\right )^{48}+48 x^{8} c_{1} \RootOf \left (\textit {\_Z}^{64} c_{1} x^{8}+12 \textit {\_Z}^{56} c_{1} x^{8}+48 \textit {\_Z}^{48} c_{1} x^{8}+64 \textit {\_Z}^{40} c_{1} x^{8}-1\right )^{40}-1}{2 c_{1} x^{7} \RootOf \left (\textit {\_Z}^{64} c_{1} x^{8}+12 \textit {\_Z}^{56} c_{1} x^{8}+48 \textit {\_Z}^{48} c_{1} x^{8}+64 \textit {\_Z}^{40} c_{1} x^{8}-1\right )^{40} \left (\RootOf \left (\textit {\_Z}^{64} c_{1} x^{8}+12 \textit {\_Z}^{56} c_{1} x^{8}+48 \textit {\_Z}^{48} c_{1} x^{8}+64 \textit {\_Z}^{40} c_{1} x^{8}-1\right )^{16}+8 \RootOf \left (\textit {\_Z}^{64} c_{1} x^{8}+12 \textit {\_Z}^{56} c_{1} x^{8}+48 \textit {\_Z}^{48} c_{1} x^{8}+64 \textit {\_Z}^{40} c_{1} x^{8}-1\right )^{8}+16\right )} \]
✓ Solution by Mathematica
Time used: 1.856 (sec). Leaf size: 673
DSolve[y[x]-3*x+(4*y[x]+3*x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,1\right ] \\ y(x)\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,2\right ] \\ y(x)\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,3\right ] \\ y(x)\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,4\right ] \\ y(x)\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,5\right ] \\ y(x)\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,6\right ] \\ y(x)\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,7\right ] \\ y(x)\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,8\right ] \\ \end{align*}