Initial Value Problems


Solve the initial value problems in Exercises 71–90.


dy/dx = 2x − 7, y(2) = 0

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.

dy/dx = (𝓍 + 1/𝓍)² , y(1)= 1

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