Problem 11
In Exercises \(11-14\) , find the solution of the differential equation \(d y / d t=k y, k\) a constant, that satisfies the given conditions. $$k=1.5, \quad y(0)=100$$
Problem 11
In Exercises \(11-20,\) solve the initial value problem explicitly. $$\frac{d y}{d x}=3 \sin x\( and \)y=2\( when \)x=0$$
Problem 11
In Exercises \(11-16,\) solve the initial value problem. Confirm your answer by checking that it conforms to the slope field of the differential equation. $$\frac{d y}{d x}=(x+2) \sin x\( and \)y=2\( when \)x=0$$
Problem 11
In Exercises \(7-12,\) use differentiation to verify the antiderivative formula. $$\int \frac{1}{1+u^{2}} d u=\tan ^{-1} u+C$$
Problem 12
In Exercises \(11-16,\) solve the initial value problem. Confirm your answer by checking that it conforms to the slope field of the differential equation. $$\frac{d y}{d x}=2 x e^{-x}\( and \)y=3\( when \)x=0$$
Problem 12
In Exercises \(11-20,\) solve the initial value problem explicitly. $$\frac{d y}{d x}=2 e^{x}-\cos x\( and \)y=3\( when \)x=0$$
Problem 12
In Exercises \(5-14,\) evaluate the integral. $$\int \frac{1-3 x}{3 x^{2}-5 x+2} d x$$
Problem 12
In Exercises \(7-12,\) use differentiation to verify the antiderivative formula. $$\int \frac{1}{\sqrt{1-u^{2}}} d u=\sin ^{-1} u+C$$
Problem 12
In Exercises \(11-14\) , find the solution of the differential equation \(d y / d t=k y, k\) a constant, that satisfies the given conditions. $$k=-0.5, \quad y(0)=200$$
Problem 13
In Exercises \(13-16,\) verify that \(\int f(u) d u \neq \int f(u) d x\) $$f(u)=\sqrt{u}\( and \)u=x^{2}(x>0)$$
