{Use of Tech} Graphing general solutions Graph several functions that satisfy each of the following differential equations. Then find and graph the particular function that satisfies the given initial condition.

f'(x) = 3x + sinx; f(0) = 3

Particular antiderivatives For the following functions f, find the antiderivative F that satisfies the given condition.

f(x) = 8x³ + sin x; F(0) = 2

Particular antiderivatives For the following functions f, find the antiderivative F that satisfies the given condition.

f(v) = sec v tan v; F(0) = 2, -π/2 < v < π/2

Particular antiderivatives For the following functions f, find the antiderivative F that satisfies the given condition.

f(x) = (3y + 5)/y; F(1) = 3. y > 0

Initial Value Problems

Solve the initial value problems in Exercises 89–92.

d^3 r/dt^3 = - cos t; r''(0) = r'(0) = 0 , r(0) = -1

Initial Value Problems

Solve the initial value problems in Exercises 71–90.

dy/dx = 2x − 7, y(2) = 0

Initial Value Problems

Solve the initial value problems in Exercises 71–90.

dy/dx = 1/x² + x, x > 0; y(2) = 1

Initial Value Problems

Solve the initial value problems in Exercises 71–90.

dy/dx = 3x⁻²ᐟ³, y(−1) = −5