29.18.14 problem 490

Internal problem ID [5088]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 490
Date solved : Monday, January 27, 2025 at 10:10:15 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.948 (sec). Leaf size: 38

dsolve((7*x+5*y(x))*diff(y(x),x)+10*x+8*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = x \left (\operatorname {RootOf}\left (\textit {\_Z}^{25} c_{1} x^{5}-2 \textit {\_Z}^{20} c_{1} x^{5}+\textit {\_Z}^{15} c_{1} x^{5}-1\right )^{5}-2\right ) \]

✓ Solution by Mathematica

Time used: 2.359 (sec). Leaf size: 276

DSolve[(7 x+5 y[x])D[y[x],x]+10 x+8 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,1\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,2\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,3\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,4\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,5\right ] \\ \end{align*}