$4\mathrm{.}2.$ Exercises

Find the general solutions, or particular solutions if given conditions, to the following differential equations.

a$.y^{\text{'}}=-2x$

g$.y^{\text{'}}+2y=2$;

$y(0)=0$

b$.,y^{\text{'}}=\frac{2y}{x}$

h$.,y^{\text{'}}-\frac{y(3t-1)}{t}=0$

c$.y^{\text{'}}+y^2=0$;

$y(0)=2$

d$.y^{\text{'}}-4y=0$;

$y(0)=10$

i$.,y^{\text{'}}=\frac{e^{x-y}}{e^x+1}$;

$y(0)=ln(ln2)$

e$.y^{\text{'}}+2y=0$;

$y(0)=0\mathrm{.}25$

j$.(co{s}^{2}x)y^{\text{'}}+(tanx)y=0$

f$.y^{\text{'}}-y=4$;

$y(0)=0$

k$.(y\sqrt[\phantom{2}]{1-x^2})y^{\text{'}}=-2$;$y(0)=2$