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Homework 5 ENGR452/CHE452/ME452 J. W. Jaworski 27 September 2017 1. Use the method of undetermined coefficients to solve ($x > 0$) (a) $x^2y'' + xy' - y = 4 + \ln x$ (b) $x^2y'' + 3xy' + y = 1 + x^{-1} - 2x^{-2}$ 2. Solve subject to the initial conditions y$^{iv}(x) - y = \text{Re} (2e^x + e^{3ix})$ y(0) = y'(0) = y''(0) = y'''(0) = 0. 3. Determine the solution of that satisfies x$^4$y'' = (y')$^2$ + 3x$^6$ y(1) = 2, y'(1) = 1. 4. Find all solutions of y\frac{d^2y}{dx^2} = 4\left(\frac{dy}{dx}\right)^2 + y^2. One of your solutions can be left in terms of a single integral.

          Homework 5
ENGR452/CHE452/ME452
J. W. Jaworski
27 September 2017
1. Use the method of undetermined coefficients to solve ($x > 0$)
(a) $x^2y'' + xy' - y = 4 + \ln x$
(b) $x^2y'' + 3xy' + y = 1 + x^{-1} - 2x^{-2}$
2. Solve
subject to the initial conditions
y$^{iv}(x) - y = \text{Re} (2e^x + e^{3ix})$
y(0) = y'(0) = y''(0) = y'''(0) = 0.
3. Determine the solution of
that satisfies
x$^4$y'' = (y')$^2$ + 3x$^6$
y(1) = 2, y'(1) = 1.
4. Find all solutions of
y\frac{d^2y}{dx^2} = 4\left(\frac{dy}{dx}\right)^2 + y^2.
One of your solutions can be left in terms of a single integral.

Homework 5
ENGR452/CHE452/ME452
J. W. Jaworski
27 September 2017
1. Use the method of undetermined coefficients to solve (x > 0)
(a) x^2y” + xy' - y = 4 + ln x
(b) x^2y” + 3xy' + y = 1 + x^-1 - 2x^-2
2. Solve
subject to the initial conditions
y^iv(x) - y = Re (2e^x + e^3ix)
y(0) = y'(0) = y”(0) = y”'(0) = 0.
3. Determine the solution of
that satisfies
x^4y” = (y')^2 + 3x^6
y(1) = 2, y'(1) = 1.
4. Find all solutions of
y(d^2y)/(dx^2) = 4((dy)/(dx))^2 + y^2.
One of your solutions can be left in terms of a single integral.

Added by Jennifer L.

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