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Problem 13

In Exercises \(11-20,\) solve the initial value problem explicitly. $$\frac{d u}{d x}=7 x^{6}-3 x^{2}+5\( and \)u=1\( when \)x=1$$

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)$$

Problem 13

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 u}{d x}=x \sec ^{2} x\( and \)u=1\( when \)x=0$$

Problem 13

In Exercises \(5-14,\) evaluate the integral. $$\int \frac{8 x-7}{2 x^{2}-x-3} d x$$

Problem 14

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 z}{d x}=x^{3} \ln x\( and \)z=5\( when \)x=1$$

Problem 14

In Exercises \(5-14,\) evaluate the integral. $$\int \frac{5 x+14}{x^{2}+7 x} d x$$

Problem 14

In Exercises \(11-20,\) solve the initial value problem explicitly. $$\frac{d A}{d x}=10 x^{9}+5 x^{4}-2 x+4\( and \)A=6\( when \)x=1$$

Problem 14

In Exercises \(13-16,\) verify that \(\int f(u) d u \neq \int f(u) d x\) $$f(u)=u^{2}\( and \)u=x^{5}$$

Problem 14

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. $$y(0)=60, \quad y(10)=30$$

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$$

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