The discussion centers on solving the differential equation \(\frac{dx}{dt}=4(x^2+1)\). Participants emphasize that dividing both sides by \(4(x^2+1)\) is the correct method, as it allows for the separation of variables without risking division by zero. Subtracting \(4(x^2+1)\) from both sides leads to an incorrect formulation, resulting in a different answer upon integration. The consensus is that division is the mathematically sound approach for this separable equation.
PREREQUISITESStudents and educators in mathematics, particularly those focusing on differential equations, as well as anyone looking to enhance their problem-solving skills in calculus.
find_the_fun said:If you have the equation [math]\frac{dx}{dt}=4(x^2+1)[/math] I sometimes get confused if i should should subtract [math]4(x^2+1)[/math] from both sides or multiply by it's reciprocal. If I subtract from both sides then I'd have 0 on the right side and that would give a different answer after integration but mathematically why would it be wrong?
find_the_fun said:If you have the equation [math]\frac{dx}{dt}=4(x^2+1)[/math] I sometimes get confused if i should should subtract [math]4(x^2+1)[/math] from both sides or multiply by it's reciprocal. If I subtract from both sides then I'd have 0 on the right side and that would give a different answer after integration but mathematically why would it be wrong?