Solving Differential Equations with Embedded Derivative Substitutions (Differential Equations 24)

How to solve Differential Equations with a unique technique of looking for a derivative of a substitution within the differential equation.

[wirito]

Professor Leonard. I know this is not the right video to post this but I wanted you to read it. I was failing statistics this semester. Failed both exams and needed 85 on the final to pass with a C. I started watching your videos on statistics on the final stretch of the semester, the distributions, hypothesis testing, confidence interval etc.

I want to say THANK YOU. I thought I wouldn’t make it but watching your videos everything started to click and thanks to you I got 87.5 on the final exam and passed the class! Now I’m going to watch the entire playlist to understand the concepts I didn’t get in class.

You have a passion for teaching and all of us viewers from all over the world will be eternally grateful :)

[Alexmar]

Professor Leonard,

you are like a mentor to me. Watching your videos (I watched Calc 1, 2, 3 and now Diff Eq) did make math clear to me. I love it how you give us your thought processes to solve all kinds of mathematical problems. You break heavy stuff and make it easy. I think this is a talent that in most cases teachers do not want to dive into. If every teacher would try to teach like you do, more people would like math.

Watching your videos makes me ask "How would Professor Leonard act if.." and it did make me tremendous effective learning stuff! I have to admit, I still struggle ( I study mech. eng) but I managed to organize my material and applying the mindset of the "How to learn math" video and I am happier than ever before!

With this information: Please give us more stuff like "How to study math". For example "How to plan a day of learning" or "How to schedule your day in university/or high school".

Thank You for making these videos and happy holidays!

[vaughnmonkey]

You just made me yell at my computer screen out of the enjoyment of math instead of frustration that has been the norm this year.

[guidofeliz]

I'm anxiously waiting for the linear algebra video lessons.

[miltonpassanha]

Dear Professor Leonard - the answer to the differential eq -
“2xsinycosydy/dx =4xsq+sinsq y…. is

y=1/2 arc cosine(1-8xsq +2Cx)

[BrainGainzOfficial]

Differential Equations is the last class I have to take to finish my B.S. in Mathematics! Looking forward to following along to your videos next semester!

[LazyChristy]

Professor Leonard, I'm just so glad that I found your channel and feel dumb for not watching earlier since the videos were long and we have a crazy pace at my university so I was looking for quick videos to memorize. I've been so frustrated because the horrible pace (along with other stressors, work, corona, economy etc.) made me lose interest in maths since I started associating it with stress rather than my love for it. I've had to cut down the pace but now I'm finally finding that interest again through watching your videos and actually learning to understand rather than just memorizing, and it makes me so happy. Thank you so so much. Once I get a good job I'm definitely supporting you on patreon, as you are supporting me now with my education. =)

[desseldrayce]

The Alexander the Great of Mathematics.

[nadeemjq]

Had my Calc 2 exam yesterday. But, I'm still gonna watch your series. That's how good you are!

[JasonWard]

12:12 "That little guy? Don’t worry about that little guy." You got me laughing meow.

[khbye]

42:50 Last question in the video:
I let v=x+e^y. It still works!
dv/dx = 1+ e^y*dy/dx

=> v*(dv/dx -1) =x - (v-x)
=> v*dv/dx - v = -v +2x
=> v*dv/dx = 2x
integrate both sides with respect to x
=> intgr[ v*dv] = intgr[2x*dx]
=> v^2/2 = x^2 + C_1
=> (x+e^y)^2 = 2(x^2 + C_1) = 2x^2 +C

[kunjbhatt]

Prof Leonard is the best prof i have ever seen! Honest, I have learned more from him than my actual profs. LOL keep this up. You helped me pass Calc 1, 2, 3 with A+. I need to give him all my tuition money.

[huligangaeddhaerika-nonan]

prof leonard to every method in diff equation: IT'S REALLY COOL!

[nikolozperadze]

This techniques is very impressive and so is the way in which you are able to explain it. 😎

[AFAbirALFA]

Im sorry if I break your heart. Professor You are a good professor thank you for helpfull videos. please continue helping the world.

[payrollpaul]

please keep posting!! Really grateful for these videos.

[furkangozupek]

Next semester I will take this course, when you finish all chapters everything will be fine for my future.thanks for everything 😀

[saltypokai]

after all those long homogenous and bernoulli examples this is a relief

[ccym]

Pro.Leonard, Could you please do the section of Partial Differential Equations? I am looking forward it. Appreciate it.

[rushikeshmoundekar]

sir, you are really Superman of mathematics