Problem 15
In Exercises \(15-18,\) solve the differential equation. $$\frac{d y}{d x}=\frac{2 x-6}{x^{2}-2 x}$$
Problem 15
In Exercises \(11-20,\) solve the initial value problem explicitly. $$\frac{d y}{d x}=-\frac{1}{x^{2}}-\frac{3}{x^{4}}+12\( and \)y=3\( when \)x=1$$
Problem 15
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 \sqrt{x-1}\( and \)y=2\( when \)x=1$$
Problem 16
In Exercises \(15-18,\) solve the differential equation. $$\frac{d u}{d x}=\frac{2}{x^{2}-1}$$
Problem 16
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 \sqrt{x+2}\( and \)y=0\( when \)x=-1$$
Problem 16
In Exercises \(11-20,\) solve the initial value problem explicitly. $$\frac{d y}{d x}=5 \sec ^{2} x-\frac{3}{2} \sqrt{x}\( and \)y=7\( when \)x=0$$
Problem 16
In Exercises \(13-16,\) verify that \(\int f(u) d u \neq \int f(u) d x\) $$f(u)=\sin u\( and \)u=4 x$$
Problem 17
In Exercises \(17-24,\) use the indicated substitution to evaluate the integral. Confirm your answer by differentiation. $$\int \sin 3 x d x, \quad u=3 x$$
Problem 17
In Exercises \(17-20,\) use parts and solve for the unknown integral. $$\int e^{x} \sin x d x$$
Problem 17
In Exercises \(11-20,\) solve the initial value problem explicitly. \(\frac{d y}{d t}=\frac{1}{1+t^{2}}+2^{t} \ln 2\) and \(y=3\) when \(t=0\)
