Use example in Differential Equation to explain the math myth (SOME PEOPLE HAVE A "MATH MIND" AND SOME DON'T.)

Answer:dx/dt=5x−3Step-by-step explanation:Example 1Solve the ordinary differential equation (ODE)dxdt=5x−3for x(t).Solution: Using the shortcut method outlined in the introduction to ODEs, we multiply through by dt and divide through by 5x−3:dx5x−3=dt.We integrate both sides∫dx5x−315log|5x−3|5x−3x=∫dt=t+C1=±exp(5t+5C1)=±15exp(5t+5C1)+3/5.Letting C=15exp(5C1), we can write the solution asx(t)=Ce5t+35.We check to see that x(t) satisfies the ODE:dxdt=5Ce5t5x−3=5Ce5t+3−3=5Ce5t.Both expressions are equal, verifying our solution.Example 2Solve the ODE combined with initial condition:dxdtx(2)=5x−3=1.Solution: This is the same ODE as example 1, with solutionx(t)=Ce5t+35.We just need to use the initial condition x(2)=1 to determine C.C must satisfy1=Ce5⋅2+35,so it must beC=25e−10.Our solution isx(t)=25e5(t−2)+35.You can verify that x(2)=1.Example 3Solve the ODE with initial condition:dydxy(2)=7y2x3=3.Solution: We multiply both sides of the ODE by dx, divide both sides by y2, and integrate:∫y−2dy−y−1y=∫7x3dx=74x4+C=−174x4+C.The general solution isy(x)=−174x4+C.Verify the solution:dydx=ddx(−174x4+C)=7x3(74x4+C)2.Given our solution for y, we know thaty(x)2=(−174x4+C)2=1(74x4+C)2.Therefore, we see that indeeddydx=7x3(74x4+C)2=7x3y2.The solution satisfies the ODE.To determine the constant C, we plug the solution into the equation for the initial conditions y(2)=3:3=−17424+C.The constant C isC=−2813=−853,and the final solution isy(x)=−174x4−853.