find the value of k for which $$y=x^{2}+k$$ is a solution to the differential equation:
$$2y-xy'=28$$
my work below

Question

find the value of k for which $$y=x^{2}+k$$ is a solution to the differential equation:
$$2y-xy'=28$$
my work below

kkutie7 · Answer

$$2y-x'y=28\rightarrow x\frac{dy}{dx}=2y-28\rightarrow $$
$$\frac{1}{2}\int\limits_{}^{}\frac{ dy }{ y-14 }=\int\limits\frac{dx}{x}\rightarrow $$
$$y=\frac{x+c+14}{e^{\frac{1}{2}}}$$
this is where I get confused.

superdavesuper · Answer

err it will be easier if u go the OTHER way....by differeniating y....

kkutie7 · Answer

uh ok...

superdavesuper · Answer

y'=2x n put it back in the diff eqn...

superdavesuper · Answer

oh it should be
y'=2x
AND
y=x^2 + k
into the DE

kkutie7 · Answer

so the answer is 14

superdavesuper · Answer

@Kkutie7 correct - good job! :)