7. Antiderivatives & Indefinite Integrals

Initial Value Problems

Solve the initial value problems in Exercises 71–90.

d³y/dx³ = 6; y″(0) = −8, y′(0) = 0, y(0) = 5

Initial Value Problems

Find the curve y = f(x) in the xy-plane that passes through the point (9,4) and whose slope at each point is 3√x.

Solve the initial value problems in Exercises 87 and 88.

87. dy/dx = 1 + 1/x, y(1) = 3

Solve the initial value problems in Exercises 87 and 88.

88. d²y/dx² = sec²x, y(0)=0 and y'(0)=1

Solve the initial value problems in Exercises 55–58.

57. d²y/dx² = 2e^(−x),y(0) = 1,y′(0) = 0

Initial Value Problems

Solve the initial value problems in Exercises 71–90.

d²r/dt² = 2/t³; dr/dt|ₜ ₌ ₁ =1, r(1) = 1

Solve the initial value problems in Exercises 53–56 for y as a function of x.

√(x² - 9) (dy/dx) = 1, where x > 3, y(5) = ln 3

Solve the initial value problems in Exercises 53–56 for y as a function of x.

(x² + 1)² (dy/dx) = √(x² + 1), where y(0) = 1

In Exercises 129–132 solve the initial value problem.

131. x dy - (y + √y)dx = 0, y(1) = 1

Solve the initial value problems in Exercises 71–90.

y⁽⁴⁾ = −sin t + cos t;

y′′′(0) =7, y′′(0) = y′(0) = −1, y(0) = 0