Solution: In 35–38 the graph of a member of a family of

QUESTION:

In Problems 35–38 the graph of a member of a family of solutions of a second-order differential equation \(d^{2} y / d x^{2}=f\left(x, y, y^{\prime}\right)\) is given. Match the solution curve with at least one pair of the following initial conditions.

(a) y(1) = 1,   \(y^{\prime}(1)=-2\)

(b) y(1) = 0,   \(y^{\prime}(-1)=-4\)

(c) y(1) = 1,   \(y^{\prime}(1)=2\)

(d) y(0) = 1,   \(y^{\prime}(0)=2\)

(e) y(0) = 1,   \(y^{\prime}(0)=0\)

(f) y(0) = 4,   \(y^{\prime}(0)=-2\)

Text Transcription:

d^2 y / dx^2 = f(x, y, y^prime)

y^prime(1)=-2

y^prime(-1)=-4

y^prime(1)=2

y^prime(0)=2

y^prime(0)=0

y^prime(0)=-2