In problem 9–12 use (5) to find the general solution of the given system.
9.
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- 1.2 Find the general solution of dy -2x6 dr +y = y-4arrow_forward(1/2)x=ax+ y= 5a In the system of equations above, "a" is a constant such that 0 < a < (1/3) . If ( x, y) is a solution to the system of equations, what is one possible value of y ?arrow_forward5. Miracle is working on her homework and thinks that she made an error in her process. What is her error? 5x? – 5x – 30 = 0 Line 1 5(x? — х — 6) %3D 0 Line 2 5(x – 2)(x + 3) = 0 5(x-2)(x+3) Line 3 5 Line 4 (x – 2)(x + 3) = 0 Line 5 x - 2 = 0 x + 3 = 0 Line 6 x = 2 x= -3arrow_forward
- Determine the solution of (2x - 3y + 2)dx + (2x - 3y + 1)dy = 0. a. 10x + 10y + ln(10x - 15y + 8)2 = c b. 10x + 10y + ln(10x - 15y - 8)2 = c c. 10x - 10y + ln(10x + 15y + 8)2 = c d. 10x - 10y - ln(10x + 15y + 8)2 = carrow_forwardTwo very large tanks A and B are partially filled with 100 gallons of brine each. Initially, 100 pounds of salt are dissolved in the solution in tank A and 50 pounds of salt are dissolved in the solution in tank B. The system is closed, since the well-mixed liquid is pumped only between the tanks as shown in the figure. 1. Use the information in the figure to construct a mathematical model for the number of pounds of salt x1(t) and x2(t) at time "t" in tanks A and B, respectively. 2. Find a relationship between the variables x1(t) and x2(t) that holds at time «t». 3. Explain why this relationship makes intuitive sense. 4. Use this relationship to help find the amount of salt in tank B at t = 30 min.arrow_forward7. Express the general solution to the following system in terms of real- 30-2 -1 1 0 210 valued functions: x': = 8³] X.arrow_forward
- 2 4 3. (b) Would you prefer to solve the above system by the method of undetermined coefficients? X' = (; )x + (;). Justify your answer.arrow_forward5. The function y₁ = r + 1 is a solution of (1-2-x²)+2(1+z)y-2yy=0. Find the general solution.arrow_forward12) Use y = [₁,2"+ to solve 2x²y" - xy + (x+1)y=0. n=0arrow_forward
- Example 1.21 y" + 5y" + 12y' + 8y = 5sin2x + 10x? - 3x + 7 private solution yo =?arrow_forward6. What is the general solution of * (x² + 2xy – 4y)dx - (2 – 8xy – 4y)dy = 0 a? - 4y? = c(x - y) x? + 2y = c(x + 2y) O Option 1 O Option 2 a? + 2y? = c(x - 2y) a? + 4y? = c(x + y)arrow_forwardPart III Obtain the particular solutions of the following: d. y(2x* - xy + y* )dx –x (2x – y)dy =0,arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,