Internal problem ID [510]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 33.
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^{\prime }-\frac {4 y-3 x}{2 x -y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.202 (sec). Leaf size: 33
dsolve(diff(y(x),x) = (4*y(x)-3*x)/(2*x-y(x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (c_{1} \RootOf \left (\textit {\_Z}^{20} c_{1} x^{4}-\textit {\_Z}^{4}+4\right )^{4}-3 c_{1}\right )}{c_{1}} \]
✓ Solution by Mathematica
Time used: 1.158 (sec). Leaf size: 336
DSolve[y'[x] == (4*y[x]-3*x)/(2*x-y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [\text {$\#$1}^5+15 \text {$\#$1}^4 x+90 \text {$\#$1}^3 x^2+270 \text {$\#$1}^2 x^3+\text {$\#$1} \left (405 x^4-e^{4 c_1}\right )+243 x^5+e^{4 c_1} x\&,1\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+15 \text {$\#$1}^4 x+90 \text {$\#$1}^3 x^2+270 \text {$\#$1}^2 x^3+\text {$\#$1} \left (405 x^4-e^{4 c_1}\right )+243 x^5+e^{4 c_1} x\&,2\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+15 \text {$\#$1}^4 x+90 \text {$\#$1}^3 x^2+270 \text {$\#$1}^2 x^3+\text {$\#$1} \left (405 x^4-e^{4 c_1}\right )+243 x^5+e^{4 c_1} x\&,3\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+15 \text {$\#$1}^4 x+90 \text {$\#$1}^3 x^2+270 \text {$\#$1}^2 x^3+\text {$\#$1} \left (405 x^4-e^{4 c_1}\right )+243 x^5+e^{4 c_1} x\&,4\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+15 \text {$\#$1}^4 x+90 \text {$\#$1}^3 x^2+270 \text {$\#$1}^2 x^3+\text {$\#$1} \left (405 x^4-e^{4 c_1}\right )+243 x^5+e^{4 c_1} x\&,5\right ] \\ \end{align*}