10.2.32 problem 33

Internal problem ID [1160]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 33
Date solved : Monday, January 27, 2025 at 04:37:21 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {4 y-3 x}{2 x -y} \end{align*}

✓ Solution by Maple

Time used: 0.165 (sec). Leaf size: 26

dsolve(diff(y(x),x) = (4*y(x)-3*x)/(2*x-y(x)),y(x), singsol=all)
 

\[ y = x \left (-3+\operatorname {RootOf}\left (x^{4} c_1 \,\textit {\_Z}^{20}-\textit {\_Z}^{4}+4\right )^{4}\right ) \]

✓ Solution by Mathematica

Time used: 2.989 (sec). Leaf size: 336

DSolve[D[y[x],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*}