DIFFERENTIAL EQUATIO S

Question

4. \( \left(x y^{2}+7 x\right) d y+x^{2}(y+1)(y-5) \cos x^{2} d x=0 \)

5. \( y\left(2 x^{2}-x y+1\right)+(x-y) d y=0 \)

6. \( y^{\prime}+\frac{y}{x+3}=\frac{1}{(x+1)(x+3)} \)

Answer 1

5. y(2x² − xy + 1)dx + (x − y)dy = 0

Check if this equation is exact,

Then we introduce a new function, u(x) to make this equation exact,

Now we solve this exact equation,