Calc AB Need Help. Find the particular solution that passes through the point shown on the graph. Here is the picture of the question

Question

Some of the curves corresponding to different values of C in the general solution of the differential equation are shown in the graph. Find the particular solution that passes through the point shown on the graph. Here is the picture of the question

2x² − y² = C

yy' − 2x = 0

x=3 y=4

Answer 1

Just plug in x=3, y=4 into the first equation and solve for C:

C=2x²-y²=2(3)²-(4)²=2*9-16=18-16=2

Since C=2 the particular solution is:

2x²-y²=2

Answer 2

Main Equation : 2x² - Y² = C

X = 3 and Y= 4

In this case, where we find x and y ww shall replace with x and y values.

2(3)² - 4² = C

C = 2(9) - 16

C = 18 -16

C = 2

Again, YY^I - 2X = 0

(4)Y^I - 2(3) = 0

4Y^I - 6 = 0

4Y^I = 6

Y^I = 6/4 = 3/2