Chapter 4 Applications of First Order Equations 4.5 Exercises cises 1-8 find a first order differential equation for the given family y(x² + y2) = c 2. exy = cy In |xy|= c(x² + y2) y = ex² + ce-x2 y = sin x + cex Show that the family of circles 4. y = x 1/2 + cx 6. y=x³ + 8. y=ex+c(1 + x²) (x-xo)² + y² = 1, -x < x0< can be obtained by joining integral curves of two first order differ cally, find differential equations for the families of semicircles (x-xo)² + y² = 1, xo < x < xo +1, -∞ (x-xo)² + y² = 1, xo-1 < x < xo, -∞ Suppose ƒ and g are differentiable for all x. Find a differential equ y=f+cg (c=constant). cises 11-13 find a first order differential equation for the given fa