$\mathrm{dsolve}\left(\mathrm{diff}\left(y\left(x\right)\,x\right)\+y\=0\right)$

Error, (in dsolve) y(x) and y cannot both appear in the given ODE.

$\mathrm{dsolve}\left(\mathrm{diff}\left(y\left(x\right)\,x\right)\+y\left(x\right)\=0\right)$

$y\left(x\right)\=\mathrm{\_C1}{\ⅇ}^{-x}$

$\mathrm{ode}:=x^2\left(\frac{{\ⅆ}^2}{\ⅆt^2}y\left(t\right)\right)-3x\left(\frac{\ⅆ}{\ⅆt}y\left(t\right)\right)\+2y\=x^2$

$\mathrm{ode}:=x^2\left(\frac{{\ⅆ}^2}{\ⅆt^2}y\left(t\right)\right)-3x\left(\frac{\ⅆ}{\ⅆt}y\left(t\right)\right)\+2y\=x^2$

$\mathrm{IC} ≔ y\left(0\right) \= 7\, \left(\mathrm{D}\left(y\right)\right)\left(1\right) \= 2$

$\mathrm{IC}:=y\left(0\right)\=7\,\mathrm{D}\left(y\right)\left(1\right)\=2$

$\mathrm{dsolve}\left(\left\{\mathrm{ode}\, \mathrm{IC}\right\}\, y\left(t\right)\right)$

Error, (in dsolve) y(t) and y cannot both appear in the given ODE.

$\mathrm{ode}:=x^2\left(\frac{{\ⅆ}^2}{\ⅆt^2}y\left(t\right)\right)-3x\left(\frac{\ⅆ}{\ⅆt}y\left(t\right)\right)\+2y\left(t\right)\=x^2$

$\mathrm{ode}:=x^2\left(\frac{{\ⅆ}^2}{\ⅆt^2}y\left(t\right)\right)-3x\left(\frac{\ⅆ}{\ⅆt}y\left(t\right)\right)\+2y\left(t\right)\=x^2$

$\mathrm{IC} ≔ y\left(0\right) \= 7\, \left(\mathrm{D}\left(y\right)\right)\left(1\right) \= 2$

$\mathrm{IC}:=y\left(0\right)\=7\,\mathrm{D}\left(y\right)\left(1\right)\=2$

$\mathrm{dsolve}\left(\left\{\mathrm{ode}\, \mathrm{IC}\right\}\, y\left(t\right)\right)$

$y\left(t\right)\=\frac{1}{2}{x}^2\+\frac{1}{2}\frac{\left(4x-14{\ⅇ}^{\frac{1}{x}}\+{\ⅇ}^{\frac{1}{x}}{x}^2\right){\ⅇ}^{\frac{2t}{x}}}{2{\ⅇ}^{\frac{2}{x}}-{\ⅇ}^{\frac{1}{x}}}-\frac{{\ⅇ}^{\frac{t}{x}}\left(-14{\ⅇ}^{\frac{2}{x}}\+x^2{\ⅇ}^{\frac{2}{x}}\+2x\right)}{2{\ⅇ}^{\frac{2}{x}}-{\ⅇ}^{\frac{1}{x}}}$